Structural evolution in three and four-layer Aurivillius solid solutions: A comparative study versus relaxor properties

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Solid State Sciences 10 (2008) 177e185 www.elsevier.com/locate/ssscie

Structural evolution in three and four-layer Aurivillius solid solutions: A comparative study versus relaxor properties Jenny Tellier a, Philippe Boullay a,*, Dorra Ben Jennet b, Daniele Mercurio a a

Laboratoire de Sciences de Proce´de´s Ce´ramiques et Traitements de Surface (CNRS UMR6638), 123 Av. Albert Thomas, Universite´ de Limoges, F-87060 Limoges Cedex, France b Laboratoire de Chimie Mine´rale Applique´e, Universite´ de Tunis El Manar, Faculte´ des Sciences, 1060 Tunis, Tunisia Received 20 June 2007; accepted 19 September 2007 Available online 26 November 2007

Abstract Two solid solutions of three-layer BaxBi4xNbxTi3xO12 (0  x  1.2) and four-layer Aurivillius compounds (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1), which both present a ferroelectric to relaxor-like transition with increasing x, were synthesized by solid state reaction. The evolution of their crystal structures, as a function of x, was performed using Rietveld refinements from X-ray powder diffraction data. As x increases, the average crystal structures become less distorted with respect to the archetypal high temperature tetragonal one and the coordination number of Bi3þ in M2O2 layers continuously changes from {4 þ 2} to {4}. The relaxor behaviour which appears in samples for a tolerance factor t > 0.96 is associated with a general static disorder in A and M sites together with the presence of some Ba2þ cations in M2O2 layers (less than 10%). Ó 2007 Elsevier Masson SAS. All rights reserved. Keywords: Bismuth oxides; Ferroelectrics; Relaxors; Structure refinement; Perovskite; X-ray diffraction

1. Introduction Aurivillius phases [1e3] are a family of compounds with the general composition Am1BmO3mþ3, the majority of them exhibit a ferroelectric behaviour at room temperature. They can be used as high temperature lead-free piezoelectric devices or as ferroelectric non-volatile memories (FeRAM) [4e7]. These perovskite-based materials can be described as the regular intergrowth of [M2O2]2þ fluorite-like layers and [Amþ1BmO3mþ1]2 perovskite blocks. Aurivillius phases are characterized by a consequential compositional flexibility of the perovskite blocks. Indeed, in the last formula, A is a 12-fold-coordination cation, like Naþ, Kþ, Ca2þ, Sr2þ, Ba2þ, Pb2þ, Bi3þ or Ln3þ; B is a 6-foldcoordination cation, e.g. Fe3þ, Cr3þ, Ti4þ, Nb5þ,Ta5þ or W6þ; and m (1  m  8) represents the number of octahedral layers in perovskite blocks. The cationic sites in the interleave * Corresponding author. Present address: CRISMAT, CNRS UMR 6508, ENSICAEN, 6 Bd. du Mare´chal JUIN, 14050 Caen Cedex, France. Tel.: þ33 (0) 2 31 45 26 10; fax: þ33 (0) 2 31 95 16 00. E-mail address: [email protected] (P. Boullay). 1293-2558/$ - see front matter Ó 2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2007.09.010

[M2O2]2þ layers are almost exclusively occupied by Bi3þ cations, forming [Bi2O2]2þ layers. At room temperature, the structure of the ferroelectric Aurivillius phases presents three main distortions from the archetypal HT paraelectric phase: two tiltings of the octahedra around the a-axis and c-axis and an atomic displacement along the polar a-axis. Crystallographic studies have demonstrated the key role of the A-site cation in the ferroelectric behaviour of these materials [8] and, at first approximation, a direct relation between the average ionic radii of the A-site cation and the temperature of the ferroelectriceparaelectric transition (TC) has been established [9]. It is thus possible to modify the ferroelectric properties by changing the chemical composition. As an illustration, the majority of the Aurivillius oxides where A ¼ Ba has a relaxor type behaviour while their analogues where A ¼ Sr, Ca and Pb are normal ferroelectrics [10]. Although this phenomenon was observed since many years, for example in BaBi2(Nb/Ta)2O9 [11], its structural origin is not yet clearly known. Some recent works have shown by means of structural studies [12,13] or computing calculations [14] that a cation

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disorder in M and A sites can exist in these compounds. Hervoches and Lightfoot [12] have evidenced this behaviour in the Bi2xSr2þxTi1xNb2þxO12 (0 < x < 0.8) solid solution and presented an exhaustive summary of related works. For these authors, the driving force for this cationic disorder is based on tolerance factor arguments, i.e. the size matching of the fluorite-like and perovskite-like blocks which, to some extent, competes with the preference of Bi3þ for an asymmetric coordination environment. Moreover, in fluorite-like layers a static disorder is also observed [12,13]. In previous papers, we were interested in the relation between the crystal structure and the change of the dielectric properties of the Aurivillius phases (classical ferroelectric behaviour to relaxor-like ferroelectric comportment). We have clearly demonstrated the key role of the tolerance factor on the A/Bi substitution in M2O2 slabs as well as the relation between the A-cation content in these slabs and the dielectric properties. In a comparative study of CaBi4Ti4O15 (ferroelectric) and BaBi4Ti4O15 (relaxor-like ferroelectric) by single crystal X-ray diffraction we have shown that Ba2þ (but not Ca2þ) cation substitutes Bi3þ in M2O2 slabs [15]. Moreover, using a global (3 þ 1)D superspace group approach, based on a modelling of the Aurivillius phases in terms of B deficient cation perovskite AB1xO3 [16], we have shown that in the pseudo-binary system Bi4Ti3O12ePbTiO3 a cationic disorder appears in the fluorite slabs with increasing Pb content (when the tolerance factor increases), i.e. when the number of layers in perovskite blocks

increases [17]. This disorder is systematically present when a ‘‘relaxor-like’’ ferroelectric behaviour occurs in the phases. In this paper we present the structural results, obtained by Rietveld analysis of powder X-ray diffraction data, for two solid solutions: BaxBi4xNbxTi3xO12 (0  x  1.2) and (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) [18,19]. They are both characterized by a change in the dielectric properties (ferroelectric to relaxor) when Ba2þ content increases. The BaxBi4xTi3xNbxO12 solid solution was first reported by Subbarao [20] and its feasibility was shown by Armstrong and Newnham [21] with a solubility limit of x ¼ 1.35. In a previous publication [18], its ferroelectric properties were measured; it was shown that a relaxor-like behaviour appears for x 0.6, whereas the compounds exhibit a normal ferroelectric behaviour for lower values of x. Moreover, Na0.5Bi4.5Ti4O15 (x ¼ 0) and BaBi4Ti4O15 (x ¼ 1) are well known members of the (Na0.5Bi0.5)1xBaxBi4Ti4O15 solid solution [2,3,6e12]. Na0.5Bi4.5Ti4O15 is known as a classical ferroelectric with TC ¼ 655  C whereas BaBi4Ti4O15 has a relaxor-like behaviour and a broad transition around 400  C [4,22]. In the solid solution (Na0.5Bi0.5)1xBaxBi4Ti4O15, Ben Janet et al. [19] have identified a ferroelectric versus relaxor behaviour with a change of comportment for x ¼ 0.8. The results of the different refinements will be focused on the structural evolution within BaxBi4xTi3xNbxO12, a three-layer Aurivillius solid solution (B2cb S.G. no. 41), and (Na0.5Bi0.5)1xBaxBi4Ti4O15, a four-layer Aurivillius solid solution

Fig. 1. Final observed, calculated and difference plots for the XRPD Rietveld refinement of Bi4xBaxTi3xNbxO12: (a) Bi3.8Ba0.2Ti2.8Nb0.2O12 and (b) Bi2.8Ba1.2Ti1.8Nb1.2O12. The set of tick marks represents the reflection associated to Bi4xBaxTi3xNbxO12.

J. Tellier et al. / Solid State Sciences 10 (2008) 177e185 Table 1 Refined atomic coordinates and atomic displacement parameters for ferroelectric Ba0.2Bi3.8Ti2.8Nb0.2O12 at room temperature with space group B2cb (no. ˚ , b ¼ 5.4228(2) A ˚ and c ¼ 33.0522(8) A ˚ 41) and cell parameters a ¼ 5.4547(2) A Wyckoff x position MeBi(1) AeBi(2) Ti(1) Ti(2) O(1) O(2) O(3) O(4) O(5a) O(5b)

8b 8b 4a 8b 4a 8b 4a 8b 8b 8b

0.023(4) 0.038(3) 0 0.010(4) 0.281(4) 0.036(4) 0.241(8) 0.006(6) 0.241(8) 0.301(5)

y

z

Uiso/Ueq ˚ 2) (A

0.0159(6) 0.9955(6) 0 0.005(2) 0.2528(18) 0.050(4) 0.25 0.979(5) 0.227(5) 0.276(4)

0.21167(4) 0.06708(4) 0.5 0.37117(13) 0.0077(6) 0.4399(3) 0.2493(8) 0.3171(4) 0.1160(5) 0.8759(5)

0.0212(5) 100 0.0175(6) 90/10 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02

Table 2 Refined atomic coordinates and atomic displacement parameters for relaxor-like Ba1.2Bi2.8Ti1.8Nb1.2O12 at room temperature with space group B2cb (no. 41) and ˚ , b ¼ 5.5149(2) A ˚ and c ¼ 33.8560(1) A ˚ cell parameters a ¼ 5.5149(2) A

Occ (%)a AeBi(2) MeBi(1) Ti(1) Ti(2) O(1) O(3) O(2) O(4) O(5a) O(5b)

For this refinement, wRobs ¼ 1.81%, wRp ¼ 9.45% and c2 ¼ 2.13. a Bi/Ba rate rounded to %.

(A21am S.G. no. 36). A comparative analysis of these evolutions in terms of both deformation of the ‘‘ideal’’ structure (archetypal high temperature tetragonal structure) and orderedisorder phenomena in the A and M cationic sites will allow to reinforce our previous arguments concerning the structural parameters which lead to the onset of the relaxor behaviour [15,17,23,24] 2. Experimental Polycrystalline samples of BaxBi4xTi3xNbxO12 (0  x  1.2) and (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) were prepared by solid state reaction. Stoichiometric amounts of BaCO3, Na2CO3, Bi2O3, TiO2 and Nb2O5 were mixed during 1 h by ball-milling in an agate planetary ball mill using acetone as liquid medium. Reaction conditions for obtaining pure powder samples of BaxBi4xTi3xNbxO12 (0  x  1.2) were 24 h at 850  C followed by another firing of 24 h at 1000  C with an intermediate regrinding. For (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1), pure phases were directly obtained after 12 h heating at 1050  C. The X-ray powder diffraction (XRPD) data were collected on a Siemens D5000 diffractometer (Cu Ka, graphite monochromator) with an angular range of 10e100 with a 0.02 step and 16 s per step.

179

Wyckoff position

x

y

z

8b 8b 4a 8b 4a 4a 8b 8b 8b 8b

0 0 0 0 0.25 0.25 0 0 0.25 0.25

0 0 0 0 0.25 0.25 0.000(6) 1 0.25 0.25

0.06646(6) 0.21325(5) 0.5 0.37024(12) 0 0.25 0.4399(3) 0.3173(4) 0.1206(7) 0.8794(7)

0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02

U33

U12

U11

U22

Uiso/Ueq ˚ 2) (A

Occ (%)a 48/52 92/8

U13

˚ 2) Anisotropic atomic displacement parameters of M and A sites (in A MeBi(1) 0.0150(8) 0.0150(8) 0.0432(15) 0 0 AeBi(2) 0.0474(12) 0.0474(12) 0.034(2) 0 0

U23 0 0

For this refinement, wRobs ¼ 3.04%, wRp ¼ 9.38% and c2 ¼ 1.88. a Bi/Ba rate rounded to %.

3. Structure refinement Structure refinements were performed using the Rietveld method with the software Jana2000 [25]. In order to limit the number of refined parameters, some constraints were imposed during the refinements. The validity of each constraint was systematically verified by comparison with the result obtained previously on BaBi4Ti4O15 (x ¼ 1) single crystal for (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) samples and with literature results on Bi4Ti3O12 (x ¼ 0) for BaxBi4xTi3xNbxO12 (0  x  1.2) samples. The same constraints were later applied for the refinement of each term of the two respective solid solutions. 3.1. BaxBi4xTi3xNbxO12 (0  x  1.2) A preliminary examination of the X-ray powder diffraction (XRPD) patterns shows that all the samples are pure phases, based on the three-layer Aurivillius phase Bi4Ti3O12.

Table 3 ˚ ) in the M2O2 layer for BaxBi4xTi3xNbxO12 (0  x  1.2) Main inter-atomic distances (A Cation

Anion

MeBi(1)

O(3) O(3) O(3) O(3) O(4) O(4) O(4) O(4) O(5a) O(5a) O(5b) O(5b)

Ferroelectric domain

1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x

Relaxor-like domain

x¼0

x ¼ 0.2

x ¼ 0.4

x ¼ 0.6

x ¼ 0.8

x¼1

x ¼ 1.2

2.201(18) 2.22(2) 2.416(19) 2.43(2) 2.54(3) 2.70(3) 3.08(3) 3.21(3) 3.63(3) 3.69(2) 3.25(2) 3.85(2)

2.19(3) 2.29(3) 2.32(3) 2.41(3) 2.69(2) 2.74(4) 3.04(4) 3.06(2) 3.66(3) 3.69(2) 3.315(19) 3.74(2)

2.22(2) 2.29(2) 2.32(2) 2.39(2) 2.68(3) 2.78(4) 3.02(4) 3.09(3) 3.66(2) 3.79(2) 3.49(2) 3.64(2)

2.261(18) 2.261(18) 2.354(19) 2.354(19) 2.77(3) 2.907(5) 2.907(5) 3.03(3) 3.72(2) 3.74(2) 3.583(18) 3.583(18)

2.28(2) 2.28(2) 2.33(2) 2.33(2) 2.86(4) 2.922(5) 2.922(5) 2.99(4) 3.75(2) 3.75(2) 3.62(2) 3.62(2)

2.3072(9) 2.3072(9) 2.3072(9) 2.3072(9) 2.930(5) 2.930(5) 2.930(5) 2.930(5) 3.70(2) 3.70(2) 3.67(2) 3.67(2)

2.3130(9) 2.3130(9) 2.3130(9) 2.3130(9) 2.946(5) 2.946(5) 2.946(5) 2.946(5) 3.69(2) 3.69(2) 3.69(2) 3.69(2)

Pseudo-symmetry in MeBi(1)eO distances is indicated in italic.

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Moreover when x increases the metric of the unit cell changes progressively from orthorhombic to pseudo-tetragonal with ˚ (B2cb S.G. no. 41). a ¼ b w 5.5 and c w 33.7 A Starting parameters for the Rietveld refinement are taken from Bi4Ti3O12 [26]. Due to the well known bad precision of oxygen coordinates obtained by XRPD in the presence of heavy atoms, BO6 octahedra are considered as pseudo-rigid bodies introducing ˚ ). slight OeO distance constraints (OeO z 2.8  0.4 A In the starting model (for x s 0), fluorite-type layers (M sites) are only occupied by Bi3þ cations. In perovskite blocks (A sites), barium and bismuth are statistically distributed on each site (with unique coordinates). The Bi/Ba rate in each A site and the Nb/Ti occupancy in B sites are fixed to their theoretical values, according to nominal composition. Atomic displacement parameters (ADPs) are refined only for A and M sites. For other atoms values are fixed throughout the whole refinement, ˚ 2 and Uiso(O2) ¼ 0.02 A ˚ 2. with Uiso(Ti4þ/Nb5þ) ¼ 0.01 A Each refinement consisted of the same parameter set including the modelling of the background, scale factor, lattice parameters, detector zero point and profile parameters (pseudo-Voigt function). In a first stage, atomic coordinates for all atoms, a unique site occupancy over A sites (Ba/Bi rate) and a common isotropic ADPs (Uiso) for A and M sites ˚ 2, the are simultaneously refined. When Uiso(A&M) < 0.03 A 3þ occupancy rates in both A and M (100% Bi ) sites are considered good and fixed. For these sites, anisotropic ADPs are used and refined individually. This is the end of the refinement ˚ 2, some in this case. On the contrary, if Uiso(A&M)  0.03 A 2þ Ba are considered to be inside the fluorite layer, so a nonzero rate of Ba2þ is introduced into M site and all occupancies are refined together with those of the A sites, using a compositional constraint. A common isotropic ADP is applied and refined. Then, in a final stage, the occupancy rates of A sites are fixed and the anisotropic ADPs are refined individually. Due to some terms that were undefined, an additional constraints have been applied, with U11 ¼ U22 and U12 ¼ U13 ¼ U23 ¼ 0, in order to estimate the direction of the atomic displacement. For every step, the atomic coordinates are systematically fixed when the values are close (less than the uncertainty) to the corresponding coordinates in F2mm space group.

(Na, Ba, Bi) cations in the A sites have been replaced by a fictitious Bi one. It means that only the number of electrons per site is refined by the occupancy of ‘‘pseudo-Bi’’ cation. The initial occupancy rate of ‘‘pseudo-Bi’’ cation is determined from the nominal composition.

3.2. (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) All the diffraction patterns can be indexed on the basis of an orthorhombic four-layer Aurivillius structure (space group A21am) and cell parameters a w 5.45, b w 5.43 and ˚. c w 41.5 A The previous strategy developed for BaxBi4xTi3xNbxO12 (0  x  1.2) has been applied in the refinement of (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) samples. Starting parameters are issued from BaBi4Ti4O15 [15]. Refinements are made from (Na0.5Bi0.5)Bi4Ti4O15 (x ¼ 0), with M sites (named Bi(1)) occupied by Bi3þ only and A sites (named Bi(2) and Bi(3)) occupied statistically by Naþ/Ba2þ/Bi3þ cations according to the composition. Moreover, in order to always limit the number of parameters to refine, and after a check on the BaBi4Ti4O15 results,

Fig. 2. Representation of Bi4xBaxTi3xNbxO12 (x ¼ 0.2 (ferro); and x ¼ 1.2 (relaxor)); projections onto ( yOz) and (xOy) plans. Double tilting of the octahedral network around the a-axis and c-axis and atomic displacement along aaxis have disappeared for x ¼ 1.2. The radii of the spheres used to represent the atomic positions correspond to the atomic displacement parameters.

J. Tellier et al. / Solid State Sciences 10 (2008) 177e185

181

Fig. 3. Final observed, calculated and difference plots for the XRPD Rietveld refinement of (Na0.5Bi0.5)1xBaxBi4Ti4O15: (a) Na0.4Ba0.2Bi4.4Ti4O15 and (b) Na0.1Ba0.8Bi4.1Ti4O15. The set of tick marks represents the reflection associated to (Na0.5Bi0.5)1xBaxBi4Ti4O15.

4. Results and discussion Typical final Rietveld plots of BaxBi4xNbxTi3xO12 series are shown in Fig. 1 (x ¼ 0.2 and 1.2). For these two compositions, the atomic positions, ADPs and occupancy rates obtained from the refinements are summarized in Tables 1 and 2 with the reliability factors. Results concerning the other samples can be seen in Supplementary materials. The inter-atomic distances in the coordination sphere of the M site are given in Table 3. The crystal structures projected onto ( yOz) and (xOy) are presented in Fig. 2. For (Na0.5Bi0.5)1xBaxBi4Ti4O15, the measured, calculated and difference diagrams resulting from the Rietveld refinements of x ¼ 0.2 (ferro) and x ¼ 0.8 (relaxor) samples are shown in Fig. 3. The final parameters are summarized in Tables 4 and 5 (see Supplementary materials for the other compositions). The inter-atomic distances in the coordination sphere of the M site are given in Table 6. The crystal structures projected onto ( yOz) and (xOy) can be seen in Fig. 4. For the two series, when x increases, and as expected by the substitution Bi3þ/Ba2þ or Bi3þ/½Naþ þ ½Ba2þ, unit cell parameters, volume and hA/MeOi average distances increase (see Figs. 5 and 6) in agreement with the ionic radii in 12˚ for Ba2þ; 1.36 A ˚ for Bi3þ (estimated fold coordination: 1.61 A 3þ þ ˚ for Na [27]. However, although the from La ) and 1.39 A evolution of V is nearly linear for the two series, the evolution of unit cell parameters differs: for low values of x, the slow increase of b compared to a leads to a pseudo-tetragonal unit cell

for BaxBi4xNbxTi3xO12 (0  x  1.2) while the metric of the unit cell remains always orthorhombic for (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) (Fig. 5). Moreover, for the three-layer ˚ solid solution, the Ti4þ/Nb5þ substitution (ionic radii: 0.64 A ˚ for Ti4þ in 6-fold coordination [25]) also for Nb5þ; 0.605 A leads to a regular increase of hBeOi average distance (Fig. 6). When x increases, the structural evolutions of the two solid solutions are very similar: the double tilting of the octahedral Table 4 Refined atomic coordinates and atomic displacement parameters for ferroelectric Ba0.2Na0.4Bi4.4Ti4O15 at room temperature with space group A21am (no. 36) ˚ , b ¼ 5.4269(2) A ˚ and c ¼ 41.013(2) A ˚ and cell parameters a ¼ 5.4530(2) A

MeBi(1) AeBi(2) AeBi(3) Ti(1) Ti(2) O(1) O(2a) O(2b) O(3) O(4) O(5a) O(5b) O(6)

Wyckoff x position

y

z

Uiso/Ueq ˚ 2) (A

8b 4a 8b 8b 8b 4a 8b 8b 8b 8b 8b 8b 8b

0.2627(12) 0.255(2) 0.2566(15) 0.242(7) 0.25 0.307(6) 0.547(4) 0.538(6) 0.5 0.292(4) 0.5 0.508(5) 0.274(5)

0.21906(4) 0 0.39500(4) 0.54906(14) 0.34644(15) 0 0.0525(5) 0.5431(4) 0.25 0.4030(3) 0.1430(5) 0.3515(5) 0.1953(3)

0.0230(7) 100 0.0178(10) 80/20 0.0168(8) 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

0 0 0 0.030(3) 0.022(4) 0.069(5) 0.352(4) 0.267(7) 0.239(12) 0.048(4) 0.292(5) 0.282(6) 0.040(6)

For this refinement, wRobs ¼ 2.27%, wRp ¼ 9.88% and c2 ¼ 1.93. a Bi/(Ba þ Na) rate rounded to %.

Occ (%)a

J. Tellier et al. / Solid State Sciences 10 (2008) 177e185

182

Table 5 Refined atomic coordinates and atomic displacement parameters for relaxor-like Ba0.8Na0.1Bi4.1Ti4O15 at room temperature with space group A21am (no. 36) and ˚ , b ¼ 5.4471(2) A ˚ and c ¼ 41.6627(9) A ˚ cell parameters a ¼ 5.4647(2) A

MeBi(1) AeBi(2) AeBi(3) Ti(1) Ti(2) O(1) O(2a) O(2b) O(3) O(4) O(5a) O(5b) O(6)

Wyckoff x position

y

z

Uiso/Ueq Occ ˚ 2) (A (%)a

8b 4a 8b 8b 8b 4a 8b 8b 8b 8b 8b 8b 8b

0.25 0.25 0.25 0.273(3) 0.25 0.301(6) 0.531(4) 0.529(6) 0.5 0.280(5) 0.5 0.5 0.263(5)

0.21964(4) 0 0.39410(4) 0.54922(12) 0.34514(13) 0 0.0510(5) 0.5435(4) 0.25 0.4032(2) 0.1448(5) 0.3516(5) 0.1955(3)

0.028 0.038 0.035 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

0 0.018(3) 0 0 0.018(4) 0.053(5) 0.325(4) 0.264(8) 0.232(11) 0.042(4) 0.281(5) 0.282(5) 0.031(6)

U11

U22

U33

U12

U13

93/7 74/26

U23

˚ 2) Anisotropic atomic displacement parameters of M and A sites (in A MeBi(1) 0.028(3) 0.026(3) 0.0362(13) 0.013(6) 0.004(7) 0.006(5) AeBi(2) 0.047(5) 0.035(4) 0.032(2) 0.009(12) 0 0 AeBi(3) 0.033(3) 0.031(3) 0.0418(17) 0.002(9) 0.000(7) 0.006(8) For this refinement, wRobs ¼ 2.33%, wRp ¼ 8.65% and c2 ¼ 1.85. a Bi/(Ba þ Na) rate rounded to %.

network around the a-axis and c-axis and the atomic displacement along the polar a-axis observable for x ¼ 0 progressively decrease (Figs. 2 and 4 and Figs. II and III in Supplementary materials). With increasing substitution of the lone-paired Bi3þ by the bigger spherical Ba2þ, the tilting of the octahedral network decreases regularly, in agreement with the Goldschmidt factor [28] (or tolerance factor) calculated for perovskite blocks which changes from 0.973 to 1.019 for m ¼ 3 series and from 0.975 to 1.003 for m ¼ 4 series. If the octahedral geometry does not seem to be drastically affected by the cationic substitution (but it is important to remember that they are treated as pseudo-rigid bodies during the refinement), on the other hand the coordination number of A sites (perovskite blocks) increases with increasing x (from {9} to {12} for Table 6 ˚ ) in the M2O2 layer for (Na0.5Bi0.5)1xBaxBi4Main inter-atomic distances (A Ti4O15 (0  x  1) Cation

Anion

MeBi(1) O(3) O(3) O(3) O(3) O(6) O(6) O(6) O(6) O(5a) O(5b) O(5a) O(5b)

Ferroelectric domain

1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x

Relaxor-like domain

x¼0

x ¼ 0.2 x ¼ 0.4 x ¼ 0.6 x ¼ 0.8

2.13(3) 2.17(3) 2.48(3) 2.51(3) 2.55(3) 2.78(4) 2.99(4) 3.19(3) 3.23(3) 3.61(3) 3.64(3) 3.68(3)

2.23(4) 2.30(4) 2.31(4) 2.38(4) 2.70(2) 2.69(3) 3.08(2) 3.10(3) 3.56(2) 3.46(2) 3.73(2) 3.56(3)

2.20(3) 2.27(3) 2.33(4) 2.40(3) 2.75(3) 2.76(2) 3.03(2) 3.05(3) 3.61(2) 3.52(2) 3.73(2) 3.64(2)

2.21(4) 2.25(4) 2.36(4) 2.39(4) 2.76(3) 2.81(3) 3.02(3) 3.07(3) 3.64(2) 3.55(2) 3.77(2) 3.67(2)

2.25(3) 2.25(3) 2.37(4) 2.37(4) 2.75(3) 2.84(3) 2.97(3) 3.07(3) 3.61(2) 3.48(2) 3.73(2) 3.61(2)

Pseudo-symmetry in MeBi(1)eO distances is indicated in italic.

x¼1 2.21(3) 2.21(3) 2.41(3) 2.41(3) 2.83(3) 2.84(3) 3.01(3) 3.03(3) 3.71(2) 3.56(2) 3.78(2) 3.63(2)

Fig. 4. Representation of (Na0.5Bi0.5)1xBaxBi4Ti4O15 (x ¼ 0.2 (ferro) and x ¼ 0.8 (relaxor); projections onto ( yOz) and (xOy) plans. The radii of the spheres used to represent the atomic positions correspond to the atomic displacement parameters.

m ¼ 3 series and from {7} to {9} in Bi(3) and stay {8} in Bi(2) for m ¼ 4 series). The higher coordination number in m ¼ 3 compounds can be explained by the higher content of barium in perovskite blocks: 50% for BaxBi4xNbxTi3xO12 (x ¼ 1); 28% for (Na0.5Bi0.5)1xBaxBi4Ti4O15 (x ¼ 1).

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Fig. 5. Evolution of cell parameters and volume with increasing value of x: (a) Bi4xBaxTi3xNbxO12 (0  x  1.2) and (b) (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1).

By reference to the ‘‘ideal’’ perovskite, the regularisation of the perovskite blocks is achieved more quickly in the vicinity of M2O2 layers (external octahedral layer) than for the internal octahedral network (see Figs. 2 and 4 and Figs. I and II in Supplementary materials). So, the fluorite layers adopt earlier a higher symmetry than the perovskite blocks. While the two typical tiltings of octahedra disappear almost simultaneously for m ¼ 3 series, these deformations decrease but always remain for m ¼ 4 series. It means that neither a tetragonal symmetry nor a disappearance of octahedral tiltings is necessary to generate a relaxor-like behaviour. Moreover, the regularisation of M2O2 layers could play a part in this phenomenon. Indeed, the existence of a pseudo-symmetry (four shorter MeO distances in Tables 3 and 5) corresponds to the onset of a relaxor behaviour for the two series (x ¼ 0.6 for m ¼ 3 and x ¼ 0.8 for m ¼ 4). The classical {4 þ 2} coordination of Bi3þ in ferroelectric Aurivillius phases transforms into {4} in relaxor ones. This change of the coordination number

seems favoured by the presence of Ba2þ cations in M2O2 layers. Electrostatic valences calculated for A and M sites (Fig. 7, bond valence sum (BVS) according to Brown method [29]) clearly show a decreasing of BVS in the vicinity of the ferroelectric to relaxor transition due to the Bi3þ/Ba2þ substitution. This is always related to the appearance of a static disorder in both A and M sites which are characterized by a high anisotropic atomic displacement (see ellipsoidal representation of atoms in Figs. 2 and 4 and ADPs in Tables 2 and 5). The particular shape of ellipsoids can be related to a strong positional disorder, and reflects different positions occupied by Ba2þ and Bi3þ. This matter has been already discussed in a previous publication [15]. 5. Conclusion Structural refinements using Rietveld analysis of X-ray powder diffraction data have been performed on three and

Fig. 6. Evolution of average distances with increasing value of x. (a) hA/MeOi and hBeOi in Bi4xBaxTi3xNbxO12 and (b) hAeOi in (Na0.5Bi0.5)1xBaxBi4Ti4O15.

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to the presence of Ba2þ in fluorite layers but limited to 10%. This is related to a ‘‘limit’’ value of t (t > 0.996 for relaxor compounds) which seems to characterize macroscopically the boundary between ferroelectric and relaxor-like domains [23]. Such static disorder can be generated by the presence of shear defects as shown previously by HREM investigations on bulk [23,24] and thin films materials [30]. The crystal structures analysis performed on the two solid solutions BaxBi4xNbxTi3xO12 (0  x  1.2) and (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1) reinforces our previous arguments [17, 23] concerning an apparent link between the apparition of the relaxor-like dielectric behaviour in Aurivillius phases and a weakening of the BieO bonds between the fluorite slab and the perovskite blocks. Also local composition fluctuations indicated by a static disorder onto both M and A sites as well as presence of non-Bi cations within the M2O2 layers appear as a typical feature of these relaxors.

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version, at doi:10.1016/j.solidstatesciences 2007.09.010. Fig. 7. Bond valence sum (BVS) calculated for A and M sites in (a) Bi4xBaxTi3xNbxO12 and (b) (Na0.5Bi0.5)1xBaxBi4Ti4O15. The significant decrease of its value in M sites is related to the presence of divalent non-Bi cations.

four-layer Aurivillius solid solutions: Bi4xBaxTi3xNbxO12 (0  x  1.2) and (Na0.5Bi0.5)1xBaxBi4Ti4O15 (0  x  1). In spite of some simplifications in the refinement parameters, validated by comparison with previous reliable results obtained on single crystals, the structural results with increasing values of x highlight the following points: (i) The global decrease of the deformations with respect to the prototype tetragonal high temperature structure with increasing values of x, and thus the increase of tolerance factor t. This shows the key role played by the Bi3þ/ Ba2þ substitution (lone-paired cation by a more voluminous and spherical cation) on this behaviour. (ii) The regularisation of the structure by reference to the ‘‘ideal ones’’ is done preferentially in M2O2 layers than in perovskite blocks. The value of m does not drastically change this general evolution which is more achieved in Bi4xBaxTi3xNbxO12 (m ¼ 3) than in (Na0.5Bi0.5)1xBaxBi4Ti4O15 (m ¼ 4). In the latter, the ferroelectric distortions remain even for x ¼ 1. The bismuth coordination number evolves in a regular and continuous way from {4 þ 2} to {4}. (iii) For x  0.6 (for m ¼ 3 series) and x  0.8 (for m ¼ 4 series) a double phenomenon appears: a pseudo-symmetry in M2O2 layers and a static disorder which implied both M and A sites. In M sites, this corresponds

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